Question

You and your friend are splitting a restaurant bill and leaving a tip. You pay half of the bill plus $5. Your friend pays half of the bill plus 25% of half the bill. You and your friend pay the same total amount. How much is half the bill?

(a) Write an equation. Let x be the cost of half the bill.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.

Answer 1

12x+5=a
12x+25% of 12x=b
25%=14

you and your friend pay the same total, a=b
If a=b,
12x+5=12x+14(12x)

First, you want to simplify.
12x+5=12x+18x

Multiply by 8 on both sides to get rid of those fractions
4x+40=4x+x

Subtract 4x on both sides to find x
40=x

Half of x so 1/2 of x

Answer is 20